# A107 Cosmic Microwave Background Radiation and The Wien Law Assignment

This week, we examine the cosmic microwave background radiation – the “CMB.” This image comes from the European Space Agency’s Planck satellite mission

Your work should be submitted via Canvas using the Exploration form:

Ex10_CMB_Form.docx

The CMB radiation arises from an early phase in the history of the universe, just at the point where the universe is cool enough (about 4000 K) for protons and electrons to combine to form hydrogen atoms. Before that, hot protons and electrons were moving too fast to combine. The loose electrons scattered light, so that light could travel only a short distance before being scattered to a new direction, and the universe appeared opaque. Once atoms formed, light could travel freely, and the universe became transparent. The light we see now as the CMB radiation comes to us directly from that time in the history of the universe when atoms first formed. This period of time in the history of the universe is known as “recombination,” and occurred about 380,000 years after the Big Bang.

Use Wien’s law to predict the wavelength of peak brightness of the thermal spectrum of the universe at the time of recombination.

Recall that we learned Wien’s Law in Exploration 4. Wien’s Law relates the wavelength of peak brightness to the temperature of a thermal spectrum.

Wavelength (in millimeters) = 2.9 / Temperature (in degrees Kelvin).

1. What is the peak wavelength of the thermal emission when protons and electrons combined in the early universe, when the temperature was about 4000 Kelvin?

2. What color would this radiation appear to human eyes?

NASA’s Cosmic Background Explorer satellite measured the spectrum of the CMB radiation shown below (the CMB radiation is in the microwave part of the electromagnetic spectrum).

3. What is the wavelength at which the CMB radiation observed today is brightest?

Use Wien’s law to determine the temperature of the CMB radiation we observe today. This time, you know the wavelength, but need to determine the temperature, so Wien’s Las is inverted for you below.

Temperature (in degrees Kelvin) = 2.9/wavelength (in millimeters).

4. What is the temperature represented by the thermal spectrum of the CMB observed today in the universe?

The ratio of the wavelength when the CMB radiation first formed to its wavelength today tells us how much the universe has expanded between then and now. This is just the wavelength today divided by the wavelength then.

5. By what factor has the universe expanded since the CMB formed when the universe was 380,000 years old?

Below is a pseudo-color image of the CMB in a typical region of sky. The red regions are areas with slightly higher CMB temperature, while the blue regions have slightly cooler temperatures. The colors exaggerate the range of temperature, since the actual range of temperature from point to point is only about 18 millionths of a degree, on average. Nonetheless, these slight differences in temperature are important.

The sizes of the high and low temperature blobs give us information about the average density of the universe.

Below are three simulations, one with enough mass to collapse the universe eventually (left), one just balanced between collapse and expansion (center), and one with too little mass to ever collapse the universe. The presence of large temperature blobs indicates that there is enough mass, in the form of both ordinary matter and dark matter, that the universe will eventually collapse again. A simulation with just small temperature blobs is a universe with too little mass to ever recollapse.

Compare the sizes and numbers of the blobs in each of the three simulation images above with the actual observations of the CMB. The left image above has fewer, larger blobs while the right image has more, smaller blobs. The size of blobs in the early Universe is what eventually determines how galaxies are distributed as the Universe evolves – just the distribution of galaxies we examined in Exploration 9. Comparing the simulations with the real observations is how astronomers can learn about conditions in the early Universe.

6. Which simulation is the best match to the CMB we actually observe? (Left, Center, or Right?)